Alternatively, plans where actions are assigned probabilistically (as opposed to fixed values) could be considered instead.[1]} For example, \(g^*(\mathbf {Z}) = \Pr ^*(A=1 | \mathbf {Z}=\mathbf {z})\)  where \(\Pr ^*(A=1 | \mathbf {Z}=\mathbf {z})\)  is an investigator-specified probability function for an action. For probabilistic plans, deterministic positivity becomes:
\(\Pr (A=1 | \mathbf {Z}=\mathbf {z}) \ge \epsilon > 0 \text{ for } \mathbf {z} \text{ where } g^*(\mathbf {Z}) > 0\) 
